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On the Formulation of Wald Tests of Nonlinear Restrictions

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Author Info
Phillips, Peter C B
Park, Joon Y

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Abstract

This paper utilizes asymptotic expansions of the Edgeworth type to investigate alternative forms of the Wald test of nonlinear restricti ons. Some formulae for the asymptotic expansion of the distribution of the Wald statistic are provided for a general case that should include most econometric applications. When specialized to the simple cases that have been studied recently in the literature, these formulae are found to explain rather well the discrepancies in sampling behavior that have been observed by other authors. It is further shown how the corrections delivered by Edgeworth expansions m ay be used to find transformations of the restrictions that accelerate covergence to the asymptotic distribution. Copyright 1988 by The Econometric Society.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 56 (1988)
Issue (Month): 5 (September)
Pages: 1065-83
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Handle: RePEc:ecm:emetrp:v:56:y:1988:i:5:p:1065-83

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  1. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-34, September. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jean-Marie Dufour & Alain Trognon, 2000. "Invariant Tests Based on M-Estimators, Estimating Functions and the Generalized Method of Moments," Econometric Society World Congress 2000 Contributed Papers 1420, Econometric Society. [Downloadable!]
  2. J. Dufour, . "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Sonderforschungsbereich 373 1995-27, Humboldt Universitaet Berlin.
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  3. Marcos A. Rangel & Duncan Thomas, 2006. "Out of West Africa: Evidence on the Efficient Allocation of Resources within Farm Households," Working Papers 0515, Harris School of Public Policy Studies, University of Chicago. [Downloadable!]
  4. Frank Kleibergen, 2004. "Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap," Econometric Society 2004 North American Summer Meetings 408, Econometric Society. [Downloadable!]
  5. Anyck Dauphin & Abdel-Rahmen El Lahga & Bernard Fortin & Guy Lacroix, 2008. "Are Children Decision-Makers Within the Household?," Cahiers de recherche 0829, CIRPEE. [Downloadable!]
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  6. Laura Crespo, 2005. "Estimation And Testing Of Household Labour Supply Models: Evidence From Spain," Working Papers. Serie AD 2005-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  7. Peter C.B. Phillips, 2003. "Vision and Influence in Econometrics: John Denis Sargan," Cowles Foundation Discussion Papers 1393, Cowles Foundation, Yale University. [Downloadable!]
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  8. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation, Yale University. [Downloadable!]
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  9. Peter C.B. Phillips, 1988. "Reflections on Econometric Methodology," Cowles Foundation Discussion Papers 893, Cowles Foundation, Yale University. [Downloadable!]
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  10. Francesco Bravo, . "Higher order asymptotics and the bootstrap for empirical likelihood J tests," Discussion Papers 00/30, Department of Economics, University of York. [Downloadable!]
  11. Stephen R. Blough, 1994. "Near common factors and confidence regions for present value models," Working Papers 94-3, Federal Reserve Bank of Boston. [Downloadable!]
  12. Adelina Gschwandtner, 2005. "Profit persistence in the 'very’ long run: evidence from survivors and exiters," Applied Economics, Taylor and Francis Journals, vol. 37(7), pages 793-806, April. [Downloadable!] (restricted)
  13. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics. [Downloadable!]
  14. Oliver Linton, 2000. "Edgeworth Approximations for Semiparametric Instrumental Variable Estimators and Test Statistics," STICERD - Econometrics Paper Series /2000/399, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  15. Helen Popper, 1995. "Term premia comovement in German, Japanese, and U.S. domestic markets," Open Economies Review, Springer, vol. 6(1), pages 49-62, January. [Downloadable!] (restricted)
  16. Samuel G. Berlinski, 2000. "Contracting-out and the Interindustry Wage Structure: Do Norms of Internal Equity Matter in Wage Determination?," Econometric Society World Congress 2000 Contributed Papers 1053, Econometric Society. [Downloadable!]
  17. Temel, Tugrul, 2001. "A Nonparametric Hypothesis Test Via The Bootstrap Resampling," 2001 Annual meeting, August 5-8, Chicago, IL 20600, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  18. Kenneth D. West & David W. Wilcox, 1993. "Some Evidence on Finite Sample Behavior of an Instrumental Variables Estimator of the Linear Quadtratic Inventory Model," NBER Technical Working Papers 0139, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  19. Marc Aerts & Gerda Claeskens, 1999. "Bootstrapping Pseudolikelihood Models for Clustered Binary Data," Annals of the Institute of Statistical Mathematics, Springer, vol. 51(3), pages 515-530, September. [Downloadable!] (restricted)
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